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Fuzzy Decision Procedures with Binary Relations

Towards A Unified Theory

  • Book
  • © 1993

Overview

Authors:
  1. Leonid Kitainik

    1. Computing Center of the Russian Academy of Science, Russia

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Part of the book series: Theory and Decision Library D: (TDLD, volume 13)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. Introduction

    • Leonid Kitainik
    Pages 1-6

  3. Common Notations

    • Leonid Kitainik
    Pages 7-10

  4. Systematization of Choice Rules with Binary Relations

    • Leonid Kitainik
    Pages 11-30

  5. Fuzzy Decision Procedures

    • Leonid Kitainik
    Pages 31-36

  6. Contensiveness Criteria

    • Leonid Kitainik
    Pages 37-45

  7. Fuzzy Inclusions

    • Leonid Kitainik
    Pages 47-102

  8. Contensiveness of Fuzzy Dichotomous Decision Procedures in Universal Environment

    • Leonid Kitainik
    Pages 103-107

  9. Choice with Fuzzy Relations

    • Leonid Kitainik
    Pages 109-136

  10. Ranking and C-Spectral Properties of Fuzzy Relations

    • Leonid Kitainik
    Pages 137-164

  11. Invariant, Antiinvariant and Eigen Fuzzy Subsets. Mainsprings of Cut Technique in Fuzzy Relational Systems

    • Leonid Kitainik
    Pages 165-181

  12. Contensiveness of Fuzzy Decision Procedures in Restricted Environment

    • Leonid Kitainik
    Pages 183-197

  13. Efficiency of Fuzzy Decision Procedures

    • Leonid Kitainik
    Pages 199-206

  14. Decision-Making with Special Classes of Fuzzy Binary Relations

    • Leonid Kitainik
    Pages 207-215

  15. Applications to Crisp Choice Rules

    • Leonid Kitainik
    Pages 217-223

  16. Applications to Decision Support Systems and to Multipurpose Decision-Making

    • Leonid Kitainik
    Pages 225-239

  17. Back Matter

    Pages 240-255
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Keywords

About this book

In decision theory there are basically two appr~hes to the modeling of individual choice: one is based on an absolute representation of preferences leading to a ntDnerical expression of preference intensity. This is utility theory. Another approach is based on binary relations that encode pairwise preference. While the former has mainly blossomed in the Anglo-Saxon academic world, the latter is mostly advocated in continental Europe, including Russia. The advantage of the utility theory approach is that it integrates uncertainty about the state of nature, that may affect the consequences of decision. Then, the problems of choice and ranking from the knowledge of preferences become trivial once the utility function is known. In the case of the relational approach, the model does not explicitly accounts for uncertainty, hence it looks less sophisticated. On the other hand it is more descriptive than normative in the first stand because it takes the pairwise preference pattern expressed by the decision-maker as it is and tries to make the best out of it. Especially the preference relation is not supposed to have any property. The main problem with the utility theory approach is the gap between what decision-makers are and can express, and what the theory would like them to be and to be capable of expressing. With the relational approach this gap does not exist, but the main difficulty is now to build up convincing choice rules and ranking rules that may help the decision process.

Authors and Affiliations

  • Computing Center of the Russian Academy of Science, Russia

    Leonid Kitainik

Bibliographic Information

  • Book Title: Fuzzy Decision Procedures with Binary Relations

  • Book Subtitle: Towards A Unified Theory

  • Authors: Leonid Kitainik

  • Series Title: Theory and Decision Library D:

  • DOI: https://doi.org/10.1007/978-94-011-1960-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1993

  • Hardcover ISBN: 978-0-7923-2367-9Published: 31 August 1993

  • Softcover ISBN: 978-94-010-4866-8Published: 23 October 2012

  • eBook ISBN: 978-94-011-1960-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XXIII, 255

  • Topics: Mathematical Logic and Foundations, Operations Research/Decision Theory

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